We return to the Stanford Stadium pricing problem, assuming a capacity of 60,000 seats and the demand curves for students and for the general public as given in Equations 5.1 and 5.2. Assume that 5% of the general public will masquerade as students (perhaps using borrowed ID cards) in order to save money.

a) Optimal prices with 10% buy down or cannibalization

b) Total revenue vs the base case without cannibalization

c) What is the maximum amount the university would be willing to pay annually for a photo ID card scanner system if there are 10 home games every year?

d) How do the optimal prices for the student and general public, and the total revenue change as the buy down percentage () changes from zero to 100%? Solve the problem for 10% increments of .

10 1 Figure 5.1 Pricing with a capacity constraint Example 51 Acume the widget eller faces the price response curve dip) 1000 - Op but can only supply a maximum 2.000 widgets during the upcoming week. Demand at the optimal unconstrained price of $8.5.000 widgets. There fore the supply contraint is binding and be needs to price at the runout price The runout price of $10.00 can be found by solving tp = 10,000 100-2,000. The general principle bhind calculating the optimal price with a supply constraint is the following The programing pic de supply chain pul to the max mw of the renow price and the constrained profitening price. As consequence, the prefa-miximuting prender a supply crestruint es ways grene shume put to she ancestrained profidecoming price The effects of different levels of capacity constraint on price and total revenue are shown in Table 5.1. For a binding capacity constraint.